41 lines
1.7 KiB
XML
41 lines
1.7 KiB
XML
<problem><script type="loncapa/python">
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R = float(random.randrange(100,200,10))
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Vrms = 120
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Vp = math.sqrt(2)*Vrms
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Pp = (Vp**2)/R
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Prms = (Vrms**2)/R
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</script><startouttext/>
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The plot shows 1/10 second of the voltage waveform of a 120V 60Hz AC
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(Alternating Current)
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power circuit, like that delivered to residences in the United States.
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<center><img src="/static/circuits/120V60Hz.gif"/></center>
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The actual voltage is \(120*sqrt(2)*cos(2*\pi*60*t)\)Volts. If we apply
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this voltage across a resistor of resistance \($R\Omega\) the resistor
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will dissipate a time-varying power.
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What is the peak power (in Watts) dissipated by the resistor?
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<endouttext/>
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<numericalresponse answer="$Pp"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
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<startouttext/>
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<br/> What is the average power (in Watts) dissipated by the resistor? (Hint: you
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compute the average power by integrating the power over one cycle of
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the waveform.)
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<endouttext/>
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<numericalresponse answer="$Prms"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
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<startouttext/>
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<br/> What would be the power (in Watts) dissipated by the resistor if the voltage
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was a constant value of 120V?
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<endouttext/>
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<numericalresponse answer="$Prms"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
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<startouttext/>
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<br/> If a time-varying voltage dissipates the same power in a resistor
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as a constant voltage would dissipate, we say that the time-varying voltage has
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the RMS value of the constant. RMS is an abbreviation for Root-Mean-Square.
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<endouttext/>
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</problem>
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